In the presence of distributed energy resources (DERs), distribution networks (DNs) operate in multiple configurations. Maintaining complete observability is essential for the monitoring of the network during operation in any configuration. This article proposes a methodology for the optimal deployment of micro-phasor measurement units ( $\mu$ PMUs) in a DN operating in multiple configurations. A composite objective function has been formulated to minimize the number of $\mu$ PMUs while maximizing measurement redundancy. The optimal solution has been obtained considering the $\mu$ PMU with or without channel limits. The constraints have been formed simultaneously to cover all operational configuration of the network while eliminating repetition. The proposed methodology has been illustrated on an eight-node reconfigurable network. It has also been verified on several reconfigurable DNs, having 33, 34, 69, 118, 123, and 167 nodes. A comparison between the proposed methodology and recently published approaches has been made. The constraints for zero-injection nodes with various network configuration has also been considered to find optimal $\mu$ PMU deployment. The obtained optimal deployment of $\mu$ PMUs with or without channel limit satisfies the criteria of complete topological observability, topological in-dependency, and maximizes the sum of topology measurement redundancy.